Q:

Prove: If n is a positive integer andn2 isdivisible by 3, then n is divisible by3.

Accepted Solution

A:
Answer and Step-by-step explanation:n > 0n² divisible by 3 ⇒ n is divisible by 3.Any number divisible by 3 has the sum of their components divisible by 3. If n² is divisible by 3,  we can say that n² can be written as 3*x.n² = 3x ⇒ n = √3xAs n is a positive integer √3x must be a integer and x has to have a 3 factor. (x = 3.a.b.c...)This way, we can say that x = 3y and y is a exact root, because n is a integer.n² = 3x ⇒ n = √3x ⇒ n = √3.3y ⇒ n = √3.3y ⇒ n = √3²y ⇒ n = 3√yWhich means that n is divisible by 3.